
MENSURATION 113
Height of the aquarium = h = 40 cm
Area of the base = l × b = 80 × 30 = 2400 cm
2
Area of the side face = b × h = 30 × 40 = 1200 cm
2
Area of the back face = l × h
= 80 × 40 = 3200 cm
2
Required area = Area of the base + area of the back face
+ (2 × area of a side face)
= 2400 + 3200 + (2 × 1200) = 8000 cm
2
Hence the area of the coloured paper required is 8000 cm
2
.
Example 5: The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find
the total cost of whitewashing all four walls of a room, if the cost of white washing is ' 5
per m
2
. What will be the cost of white washing if the ceiling of the room is also whitewashed.
Solution: Let the length of the room = l = 12 m
Width of the room = b = 8 m
Height of the room = h = 4 m
Area of the four walls of the room = Perimeter of the base × Height of the room
= 2 (l + b) × h = 2 (12 + 8) × 4
= 2 × 20 × 4 = 160 m
2
.
Cost of white washing per m
2
= ' 5
Hence the total cost of white washing four walls of the room = ' (160 × 5) = ' 800
Area of ceiling is 12 × 8 = 96 m
2
Cost of white washing the ceiling = ' (96 × 5) = ' 480
So the total cost of white washing = ' (800 + 480) = ' 1280
Example 6: In a building there are 24 cylindrical pillars. The radius of each pillar
is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of
all pillars at the rate of ' 8 per m
2
.
Solution: Radius of cylindrical pillar, r = 28 cm = 0.28 m
height, h = 4 m
curved surface area of a cylinder = 2πrh
curved surface area of a pillar =
= 7.04 m
2
curved surface area of 24 such pillar = 7.04 × 24 = 168.96 m
2
cost of painting an area of 1 m
2
= ' 8
Therefore, cost of painting 1689.6 m
2
= 168.96 × 8 = ' 1351.68
Example 7: Find the height of a cylinder whose radius is 7 cm and the
total surface area is 968 cm
2
.
Solution: Let height of the cylinder = h, radius = r = 7cm
Total surface area = 2πr (h + r)